Asked by Zu
what is the difference between csc (1/sqrt 2) and sin^-1 (1/sqrt 2) and determine their values
Answers
Answered by
oobleck
csc(1/√2) is very unusual. It is 1.5393...
1/√2 is not an angle you see very often.
sin<sup><sup>-1</sup></sup>(1/√2) = π/4
It is an angle whose sine is 1/√2
since csc(π/4) = √2,
csc<sup><sup>-1</sup></sup>(√2) = π/4
In general,
sin<sup><sup>-1</sup></sup> x = csc<sup><sup>-1</sup></sup> 1/x
1/√2 is not an angle you see very often.
sin<sup><sup>-1</sup></sup>(1/√2) = π/4
It is an angle whose sine is 1/√2
since csc(π/4) = √2,
csc<sup><sup>-1</sup></sup>(√2) = π/4
In general,
sin<sup><sup>-1</sup></sup> x = csc<sup><sup>-1</sup></sup> 1/x
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